The Colombia goalkeeper has shelved plans to leave this summer.
Wenger explained: "It was not easy, because of course all these players want to play.
"They are top-level players, they want to go to the World Cup but he will get a number of games here and he will fight with Petr Cech. The fight is quite open. At the moment I play Petr Cech but this battle is not won definitely by Petr Cech because I rate Ospina highly and, anyway, we play other competitions and he will play."